Finite-element analysis of a static fluid–solid interaction problem

Rodolfa Araya, Gabriel Barrenechea, Fabrice Jaillet, Rodolfo Rodriguez

Research output: Contribution to journalArticle

Abstract

This paper deals with a fluid–solid interaction problem inspired by a biomechanical brain model. The problem consists of determining the response to prescribed static forces of an elastic solid containing a barotropic and inviscid fluid at rest. The solid is described by means of displacement variables, whereas displacement potential and pressure are used for the fluid. This approach leads to a well-posed symmetric mixed problem, which is discretized by standard Lagrangian finite elements of arbitrary order for all the variables. Optimal-order error estimates in the H1- and L2-norms are proved for this method. A residual a posteriori error estimator is also proposed, for which efficiency and reliability estimates are proved. Finally, some numerical tests are reported to assess the performance of the method and that of an adaptive scheme based on the error estimator.
LanguageEnglish
Pages886-913
Number of pages28
JournalIMA Journal of Numerical Analysis
Volume31
Issue number3
Early online date9 Apr 2010
DOIs
Publication statusPublished - 2011

Fingerprint

Fluid-solid Interaction
Finite Element
Finite element method
Fluid
A Posteriori Error Estimators
Fluids
Error Estimator
Mixed Problem
Brain models
Error Estimates
Norm
Arbitrary
Estimate
Model
Brain
Standards

Keywords

  • fluid–solid interaction
  • adaptive scheme
  • a priori and a posteriori error estimates
  • finite elements
  • biomechanical brain model

Cite this

Araya, Rodolfa ; Barrenechea, Gabriel ; Jaillet, Fabrice ; Rodriguez, Rodolfo. / Finite-element analysis of a static fluid–solid interaction problem. In: IMA Journal of Numerical Analysis. 2011 ; Vol. 31, No. 3. pp. 886-913.
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Finite-element analysis of a static fluid–solid interaction problem. / Araya, Rodolfa; Barrenechea, Gabriel; Jaillet, Fabrice; Rodriguez, Rodolfo.

In: IMA Journal of Numerical Analysis, Vol. 31, No. 3, 2011, p. 886-913.

Research output: Contribution to journalArticle

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